This invention relates to solar power and conversion and more particularly to a reflective surface surrounding a solar radiation intercepting surface.
Power generation from renewable energy sources must become significantly more prevalent if humanity is to continue expecting a high standard of living. Being the most abundant source of renewable energy, sunlight is often used as “fuel” in photovoltaic and solar-thermal energy conversion systems or in systems combining both system types. Solar photovoltaic systems directly convert the incident solar radiation into electricity; however, the solar cell also converts part of the solar energy into heat due to inherent cell irreversibility. Solar thermal energy conversion systems first convert the incident solar radiation into a terrestrial heat source. Depending on the application the heat can directly be used for residential space heating or to provide solar hot water or as commercial process heat. Additionally, the heat source can be combined with a heat engine such as indirect mechanical (e.g., conventional compression-expansion cycle) or direct power conversion units (e.g., thermophotovoltaic, thermoelectric, or thermionic converter).
A high power conversion unit efficiency of a solar thermal power conversion system can only be achieved if the solar receiver provides the heat to the heat engine at a high temperature. Consequently, the solar receiver needs to be raised to a high temperature, which requires a high solar receiver efficiency to maximize the overall system efficiency. This is not a trivial task, especially at high solar receiver temperatures, when the infrared (IR) radiation heat losses rise sharply (FIG. 1). The spectra of the energy flux of the thermal emission qem are strongly temperature-dependent and cover a longer wavelengths range than the incoming solar energy flux qsol=OC·IAM1.5D (OC is the solar concentration) [1]:
                                          q            em                    =                                    πsin              2                        ⁢                          θ              em                        ⁢                                          ∫                0                λ                            ⁢                                                                                          2                      ⁢                                              hc                        2                                                                                    λ                      5                                                        ·                                                            ɛ                      ⁡                                              (                        λ                        )                                                                                    (                                                                        exp                          ⁡                                                      (                                                                                          hc                                /                                λ                                                            ⁢                                                                                                                          ⁢                                                              k                                B                                                            ⁢                                                              T                                abs                                                                                      )                                                                          -                        1                                            )                                                                      ⁢                                                                  ⁢                d                ⁢                                                                  ⁢                λ                                                    ,                            (        1        )            where Tabs is the absorber temperature, kB and h is the Boltzmann and Planck constants, respectively, θem is the angle (measured from the normal) within which the absorber emission is contained, and ε(λ) is the average (over the emission angle) of the directional surface emittance as a function of wavelength. By Kirchhoff's law, θem is also the maximum angle within which the absorber can receive incoming solar radiation. For a directionally-isotropic solar receiver, θem=90° the spectral hemi-spherical receiver emittance ε(λ) is equal to the spectral hemispherical receiver absorptance α(λ).
Traditionally, high solar receiver efficiencies have been achieved by using a blackbody surface to absorb the complete solar spectrum combined with large solar concentration [1], which helps to counteract radiative heat losses due to high IR emittance of the receiver (FIG. 1). Solar concentrating systems use mirrors or lenses to concentrate a large area of sunlight onto a small receiver area. Concentration of the sunlight increases the angle θi subtended by the sun at the absorber surface. The direct component of terrestrial sunlight (one sun, OC=1) is incident within θi=0.267° to the surface normal, and to achieve the maximum concentration of sunlight, OC=sin−2 θi=46050, the receiver must accept radiation in all directions (θem=90°). An alternative way to improve the energy conversion efficiency is to suppress the IR radiative heat losses by using spectrally-selective surfaces that provide high absorption in the visible and near-IR but low emission in the far-IR [2]. Yet, another little explored path is using directionally-selective surfaces [2, 3], which can enable reaching high absorber temperature via suppressing emission at large angles θ>θi, which reduces radiative heat losses without affecting absorption of sunlight as long as the sunlight is incident with an angle to that subtended by the sun at the absorber surface θem=θi is equivalent to the maximum concentration of the sunlight [4].
The top row of plots in FIG. 2 compares the effect of the control parameters discussed above, namely, solar concentration OC, emission angle θem and emission bandwidth λε[0,λem] on the maximum temperature Tabs to which the absorber can be raised. The temperature is calculated from the energy balance at thermal equilibrium qsol=qem−qamb, assuming Tamb=0 (due to much lower temperature of the ambient) and a perfect mirror on the shadow side of the absorber. As expected, the increase of the solar concentration (top left) and reduction of the emission angle (top right) both result in the increase of the absorber temperature. Reduction of the emission bandwidth first leads to the temperature increase owing to suppression of the IR radiation losses (top center). The temperature eventually peaks in the visible before dropping again due to the reduced absorption of the incident sunlight. For the case of the directionally-selective surface, the effective emittance of the solar absorber is also plotted, which in this case is assumed to be frequency-independent (ε(λ)=1) yet angularly-selective: εeff=ε·sin2 θem. The bottom row in FIG. 2 shows the effect of the same parameters on the limiting detailed balance efficiency [5,6] of a single-junction PV cell.
The heat that is provided by the solar receiver to the heat engine for the conversion to electricity is limited by the incident solar intensity, optical concentration and the IR radiation heat loss which is dependent on the receiver temperature. The optothermal efficiency ηot [7] can be expressed as
                              η          ol                =                                            τα              sol                        ⁡                          (                              1                -                                                      σ                    ⁡                                          (                                                                        T                          abs                          4                                                -                                                  T                          amb                          4                                                                    )                                                                            OC                    ·                    τ                    ·                                                                  α                        sol                                            /                                              ɛ                        eff                                                              ·                                          q                      sol                                                                                  )                                .                                    (        2        )            
Above, τ is the optical transmittance of the concentrator (e.g. lens), αsol is the absorptance and εeff the effective total hemispherical emittance of the solar absorber, and σ is the Stefan-Boltzmann constant.
It should finally be noted that these control parameters can also be used to improve the efficiency of the conversion of solar energy into electricity via a photovoltaic (PV) cell as shown in the bottom row of FIG. 2. As will be discussed below, the three major channels of losses that limit the overall efficiency of the PV cell are the band-edge thermalization of charge carriers in the PV cell, the loss of low-energy photons that cannot generate electron-hole pairs, and emission losses due to radiative recombination of electron-hole pairs. FIG. 2 shows the efficiency of the single-junction PV cell as a function of the three control parameters, i.e., solar concentration (bottom left), PV cell surface spectral selectivity (bottom center) or PV cell surface angular selectivity (bottom right). As can be seem from these plots, similarly to the solar-thermal converter case shown in FIG. 1, either increase of the solar concentration or reduction of the directional emittance boost the PV cell conversion efficiency, while the efficiency as a function of the material bandgap peaks in the near-IR and drops off in shorter and longer wavelength ranges.
The disclosed solar receiver cavity is an example of the implementation of the third approach discussed above, namely, the introduction of a directional (or angular) selectivity of the absorber surface to reduce the effective IR emittance and thus to enable high optothermal receiver efficiencies at low optical concentration. Using angularly-selective surfaces to improve the performance of solar-thermal systems has been investigated in a number of papers [2, 3], although physical devices for actually achieving an angularly-selective surface has not been proposed. Angular selectivity using photonic crystals has been theoretically investigated for PV applications [8], however, with the goal to achieve better acceptance rather than to limit the emittance at larger angles. Furthermore, it would be highly desirable to find simpler, cheaper solutions than photonic crystals, which require sophisticated design and precise nanofabrication.